Dynamics of continued fractions and kneading sequences of unimodal maps
arXiv:1012.2131
Abstract
In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.
arXiv comment21 pages, 3 figures. New section added with additional results and applications. Figures and references added. Introduction rearranged